Monte Carlo Simulations of Shear‐Thinning Flow in Geological Fractures

The hydraulic behavior of fractured rocks under shear-thinning flow is a challenging topic of interest in several fields, related either to environmental remediation or to natural resources recovery. The compound effect of fluid rheology and medium heterogeneity strongly affects flow and transport in fractured geological formations. Here, a stochastic analysis is conducted via Monte Carlo simulations to investigate the flow of shear-thinning fluids in fractures subjected to both natural and forced flow, considering different fracture dimensions, for a spatial correlation of the fracture that is an intrinsic parameter of the geological formation, independent of the fracture size. Considering the lubrication approximation, a generalized Reynolds equation for shear-thinning fluids is solved using an ad hoc, finite volume-based, numerical scheme. The influence of the rheology and aperture field heterogeneity on ensemble statistics of the velocity components and magnitude, as well as apparent fracture-scale transmissivity, is quantified over 103 fracture realizations. The probability density functions (PDFs) and relative confidence intervals, obtained by averaging over the statistics, are analyzed to characterize the apparent transmissivity transition from Newtonian to shear-thinning regime. The autocorrelation functions of velocity components are computed to understand the impact of rheology on spatial correlations the flow. Velocity components exhibit narrow PDFs with nearly exponential decay. More elevated pressure gradients emphasize the shear-thinning behavior, inducing a more pronounced flow localization, under otherwise identical conditions. This translates at the scale of the fracture into a larger apparent transmissivity as compared to the same configuration with Newtonian rheology, by orders of magnitude.